Plasmas: energy distribution

Figure C2.13.2. Electron energy distributions/(U) for a mean electron energy of 4.2 eV, Maxwell distribution (M), Dmyvesteyn distribution (D) and a calculated distribution (Ar) for an Ar plasma [12].

Gorse C and Capitelli M 1996 Non-equilibrium vibrational, electronic and dissociation kinetics in molecular plasmas and their coupling with the electron energy distribution function NATO ASI Series C 482 437-49... 

Figure 13. Electron energy distribution functions of a CH4/H2 plasma as a function of pressure, (a) 50 mTorr. (b) 40 mTorr. (c) 30 mTorr. (d) 20 mTorr. (e) 10 mTorr. Reprinted with permission from [88], K. Okada et al., J. Vac. Sci. TechnoL, A 17, 721 (1999). 1999, American Institute of Physics.

Electron energy distribution function The distribution function of electrons in a plasma. That of a low-pressure radiofrequency plasma generally consists of two Maxwellian distributions, that is, fast and slow electrons. 

For low-pressure plasmas containing mainly inert gases the electrons can be characterized by a Maxwellian electron energy distribution function (EEDF). How-... 

In silane discharges several ions are observed to be involved in a charge exchange process, and therefore maxima in their ion energy distribution at distinct energies are observed. The charge carrier density and the plasma potential that result from the fit of the lED allow for the quantification of the related parameters sheath thickness and ion flux. This method has been be used to relate the material quality of a-Si H to the ion bombardment [301. 332] see also Section 1.6.2.3. 

In Equation 3, e and m are the impinging electron energy and mass, (e) is the reaction cross section, and / (e) is the electron energy distribution function. Of course, if an accurate expression for fie) and if electron collision cross sections for the various gas phase species present are known, k can be calculated. Unfortunately, such information is generally unavailable for the types of molecules used in plasma etching. 

Figure 7. Representation of the parameter problem in plasma processes. The symbols n, /(e), TV, and r are electron density, electron energy distribution, gas density, and residence time for molecules in the plasma volume, respectively. (Reproduced with permission from Ref. 32.)...

Fig. 2.1. Representation of the parameter problem in plasma-surface interaction. n,-electron density, f(E)-electron energy distribution, N-gas density, x-residence time for gas molecules in plasma volume...

Observational evidence for the dynamic mass-flow phase includes (A) light-curves where the secondary eclipse becomes deeper at shorter wavelengths (Kondo et al. 1985), (B) the non-monotonic variation of the spectral energy distribution which is pronounced in the ultraviolet (Kondo et al. 1985), and (C) continued presence, both inside and outside the eclipses, of emission features observed in beta Lyrae (Hack et al. 1977). Phenomena (A) and (B) have been attributed to the presence of variable, optically-thick, extrastellar plasma. 

All the work just mentioned is rather empirical and there is no general theory of chemical reactions under plasma conditions. The reason for this is, quite obviously, that the ordinary theoretical tools of the chemist, — chemical thermodynamics and Arrhenius-type kinetics - are only applicable to systems near thermodynamic and thermal equilibrium respectively. However, the plasma is far away from thermodynamic equilibrium, and the energy distribution is quite different from the Boltzmann distribution. As a consequence, the chemical reactions can be theoretically considered only as a multichannel transport process between various energy levels of educts and products with a nonequilibrium population20,21. Such a treatment is extremely complicated and - because of the lack of data on the rate constants of elementary processes — is only very rarely feasible at all. Recent calculations of discharge parameters of molecular gas lasers may be recalled as an illustration of the theoretical and the experimental labor required in such a treatment22,23. ... 

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